On the irrationality measure of the number $\log 5+\frac{\pi}{2}$ and some other numbers

In this paper we find estimates for irrationality measures of the number $\log5+\frac{\pi}{2}$ and the values of the function $\arctan x$ in points $\frac{1}{n}$ where $n \in{\mathbb N}$, $n\geq3$.